Electronic Theses and Dissertations




Zhengfeng Liu



Document Type

Dissertation (Access Restricted)

Degree Name

Doctor of Philosophy


Mathematical Sciences


Applied Statistics

Committee Chair

Wai-Yuan Tan

Committee Member

Seok P. Wong

Committee Member

Lih-Yuan Deng

Committee Member

Xiaoping Xiong


This dissertation endeavors to reveal the effect of an antiretroviral therapy by modeling viral dynamics of HIV-1 infection. To accomplish the difficult goal, we develop a stochastic model to study the viral dynamics of HIV-1 infection in the antiretroviral treatment. The model characterizes the viral dynamical system of HIV-1 infection by a complex setting of time-varying or constant parameters and describes the stochastic process of viral dynamics in the antiretroviral treatment by a group of stochastic difference equations with respect to the state variables which are the random number of different strains of HIV-1 or different types of virus producing cells. We find a group of optimized values of governing the viral dynamics for the model parameters by means of the genetic algorithm under certain boundary conditions. The viral load and mutation frequency of the drug-resistant HIV-1 predicted by the numerical solutions for the expected number of state variables can thus fit the clinic data to a certain degree. We further devise an extended Kalman filter and apply the multilevel Gibbs sampling to identify the stochastic features of viral dynamics, which are generally realized by combining the different sources of information both from the stochastic model and observation model in the so-called state space modeling. As a result we are capable of understanding what might happen in viremia for a HIV-1-infected individual in the antiretroviral therapy and finally get to know how the drug-resistant HIV-1 emerged and became dominant in the plasma viral population, which is pertinent to the data from the AIDS patient. Based on our study, we propose a hypothesis for HIV-1 pathogenesis when suffered from drug intervention. Our hypothesis indicates that HIV-1 infection should share some common features in viral infection by any other species of viruses, especially retroviruses, except that the target cells are CD4+ T cells crucial in the immune system. It reflects more evidences of hypothesis "immune activation" in the HIV-1 pathogenesis that has gained popularity in current AIDS research. It is worthy while to be incorporated into mathematical models on viral dynamics in other situations of antiretroviral therapy and accordingly needs more examinations.


Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.